Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#4176 |
| Fitting | C4×#731 ⋊ C2 |
| Sylow | #731 ⋊ D4 |
86 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2^2,3,2,3^3|b^2=d,c^3=g^2,b^a=bd,e^a=e^2,f^a=f^2g,e^c=ef,f^e=fg61 conjugacy classes — view the full character table.
| maximal subgroup of | #13046431, #13046432, #13046435, … |
| maximal normal subgroup of | #13046431, #13046432, #13046435, … |
| maximal quotient of | #13046565, #13046568, #13046569, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 135);